Assignment can be done in many ways. One, which you have seen, is after publishing, you can select the icon for assignment from the published packages popup that comes up. And that same published packages dialog can be accessed at any time after the content has been published by selecting the “three dot menu” in the upper left of the editor window and selecting “Published Packages” button. This shows you every type of publish you’ve done in the past.
That same “Published Packages” menu item can be accessed from the dashboard by selecting the three dot menu in the upper right of a scenario card that you get when you mouse over it.
Additionally, you can go to an individual user in the users tab, click on the three dot menu for the user, and select any scenario you wish to assign to them there. The same also applies to the groups area, you can edit a group and assign content to the group there as well. This is also where you can see what “Jane Doe” has assigned to her, just click on Jane Does user menu, and you will see her assignments.
So, lots of choices on how and where you can assign content to users and groups.